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A billiard ball of radius R is initially at rest on a horizontal table. A cue stick delivers a horizontal impulse J at a height 2R/3 below the centre of the ball. The ball acquires initial translational speed v0. The coefficient of kinetic friction between ball and table is muₖ. Which of the following is/are correct?
- Immediately after the hit, kinetic friction acts in the negative x-direction (opposing translation)
- Immediately after the hit, kinetic friction acts in the positive x-direction (aiding translation)
- The ball immediately begins pure rolling after the hit
- The initial angular velocity of the ball is 5*v0/(3*R)
Correct answer: Immediately after the hit, kinetic friction acts in the positive x-direction (aiding translation)
Solution
The impulse is applied below the centre, producing a backspin sense relative to forward rolling. The contact point moves backward relative to ground, so friction acts forward (positive x). The ball does not immediately roll without slipping.
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